Abstract:We give a new characterization of the cardinal invariant
$\mathfrak {d}$
as the minimal cardinality of a family
$\mathcal {D}$
of tall summable ideals such that an ultrafilter is rapid if and only if it has non-empty intersection with all the ideals in the family
$\mathcal {D}$
. On the other hand, we prove that in the Miller model, given any family
$\mathcal {D}$
of analytic tall p-ideals suc… Show more
“…This ideal (and its generalizations) have been extensively studied in the past. To learn more, the reader may consult [12,21,25,24,33,35,39,41]. We now proceed to prove the following: By combining Propositions 67 and 92, we get the following:…”
Section: Lemma 63 Let I Be a Tall Ideal (S A) A Nice Pair Such That |...mentioning
We continue with the study of the Katětov order on MAD families. We prove that Katětov maximal MAD families exist under
$\mathfrak {b=c}$
and that there are no Katětov-top MAD families assuming
$\mathfrak {s\leq b}.$
This improves previously known results from the literature. We also answer a problem form Arciga, Hrušák, and Martínez regarding Katětov maximal MAD families.
“…This ideal (and its generalizations) have been extensively studied in the past. To learn more, the reader may consult [12,21,25,24,33,35,39,41]. We now proceed to prove the following: By combining Propositions 67 and 92, we get the following:…”
Section: Lemma 63 Let I Be a Tall Ideal (S A) A Nice Pair Such That |...mentioning
We continue with the study of the Katětov order on MAD families. We prove that Katětov maximal MAD families exist under
$\mathfrak {b=c}$
and that there are no Katětov-top MAD families assuming
$\mathfrak {s\leq b}.$
This improves previously known results from the literature. We also answer a problem form Arciga, Hrušák, and Martínez regarding Katětov maximal MAD families.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.